Sky 1 is not known for its original comedy, but since appointing the BBC's head of comedy commissioning, Lucy Lumsden, as its first head of laffs, the channel is making a determined effort in this arena. The early fruits of her labour could be seen with a series of Bafta-nominated shorts at Christmas – but Trollied is the first sitcom.

Anyone who saw the trailers for the show might have been forgiven a sense of déjà vu. For there were Jane Horrocks and Mark Addy in a supermarket. Only now they're staff rather than customers, and working in the budget paradise of Valco rather than advertising Tesco. But, you know, every little helps, and a sense of familiarity as a series begins is a boon, as it invites immediate buy-in.

While Horrocks is the star, as desperately insecure interim deputy manager Julie, and many of the narrative arcs swing around to include her, it is apparent that this is an ensemble piece as soon as the show begins with an excellent pastiche of Asda's advertising, as staff members mumble something ridiculous to camera about the company's commitment to excellence, or plug a line. As Leighton (bright newcomer Joel Fry) proudly puts it, "We have 17 varieties of poppadoms."

Some terrific double acts glue the fast-paced, quick-cut scenes, notably Lorraine Cheshire and Lesley McKeever as customer-service helpers Sue and Linda (revealing the dull-but-let's-make-the-most-of-it aspect of the job), and butchers Mark Addy and Nick Blood as lifer Andy and ambitionless youngster Kieran. And Kieran's relationship with checkout girl Katie (Chanel Cresswell) is clearly being lined up as this series' Office Tim and Dawn.

The writers' credits span from Big Train to Smack the Pony and Man Stroke Woman – and while Trollied lacks any of their surrealism, it certainly has a fair daub of their deliberate awkwardness, alongside some impressive characterisation.

Some of the humour is too broad to fully hit the mark – much of it relating to Julie's unrequited feelings for her manager – but there is definite promise here, for both Trollied and Sky 1's comedic undertaking.

It looked as though there might be some laughs to be had in First Cut's Superheroes of Suburbia, too. It was hard not to snigger at least a little at 27-year-old Will, aka The Dark Spartan. He dresses up in police riot gear and a helmet straight out of 300 to patrol the streets of the English Riviera as "Torbay's only real-life superhero". Let's not worry about whether Torbay needs a superhero – the police seem to be doing just fine without him – let's ask how effective Will has been. "If I could stop some major crime boss in Torbay or a massive drug syndicate, that would be fantastic," he asserts. Certainly would – although he admits he's yet to stop any crimes at all, and it doesn't help that his wife sees him off for the night by telling him: "Be safe. Don't do anything I wouldn't do."

But, just as we're about ready to mock, here comes the stinger: Julie, the Spartan's wife, is concerned that, unlike the police, her husband is patrolling without training, without back-up – and seemingly without any clue as to what dangers might actually face him. What's more, he's doing it to escape tragedy. For Julie has suffered from anxiety attacks, depression and dizziness since a head injury five years ago – and Will has had to do all the household chores along with his work and caring for their baby ever since. At one point he walked out, unable to cope; now he says his armour protects him not just physically, but psychologically, too: "What affects Will doesn't necessarily affect the Dark Spartan."

Just as serious about their duties are teenage comic aficionado Kieran from Billingham, North Yorkshire, aka Noir; and Yeovil's The Shadow (whatever made him change his name from Ken?), a 33-year-old ex-Army martial arts expert who seems to base his ninja crime-fighting around the ability to jump out of a bush and shout "Boo!" at wrongdoers. The Shadow, it emerges, is making up for being bullied at school; Noir, meanwhile, just wants to connect. Wishing to help a local girl, whose mugging he has read about in the Billingham Gazette, he tries to investigate. But, as an Asperger's sufferer, he cannot even get past the idea of talking to people about it before being struck by a panic attack.

What could have been risible – not least when Will interviews potential sidekick Black Void, a Spider-Man-style figure hampered only by his irritable bowel syndrome – is treated sympathetically.

If Sky 1 can pitch its comedy as well as film-maker Christian Watt has pitched this documentary, it'll be on to a winner.